Euro Area and European Union GDP Flash Estimates at 30 Days · Euro Area and European Union GDP...

Euro Area and European Union GDP Flash Estimates at

30 Days

Arto Kokkinen (European Commission, Luxembourg)

Hans Wouters (European Commission, Luxembourg)

Paper prepared for the 34

th IARIW General Conference

Dresden, Germany, August 21-27, 2016

Session 7F: Meeting the Measurement Challenges of Official Economics Statistics Offices IV

Time: Friday, August 26, 2016 [Morning]

EUROPEAN COMMISSION EUROSTAT Directorate C: National Accounts, Prices and Key Indicators Unit C-2: National accounts – Production

Euro area and European Union GDP flash

estimates at 30 days

Authors: Arto Kokkinen, Hans Wouters (1)

Paper prepared for the 34th General Conference of the International Association for

Research in Income and Wealth (IARIW) 2016 in Dresden, August 21–27, 2016.

Session 7F on "Meeting the Measurement Challenges

of Official Economics Statistics Offices"

(1) Eurostat, Unit C2 National accounts - Production

Abstract

GDP growth is one of the most followed National Accounts variables. At best, economic decision making

would need the data real-time. This, though, is not possible because of the need for collecting and analysing

the basic statistical information. Therefore, a reasonable request from the decision-makers is to have the data

available as soon as possible after the end of the quarter. However, there is a delicate balance between the

speed of publication and accuracy of the early estimate.

This paper shows how Eurostat with a group of EU Member States has managed meeting the challenge to

produce high quality data on GDP growth for the EU and the euro area at an advanced timeliness of 30 days

after the quarter-end. The aim of the paper is to address the request of the statistical and scientific world to

provide transparency and to better understand the development and test process of new statistical products in

official statistics, more concretely regarding the new GDP t+30 flash estimation.

The paper elaborates the statistical methods that Eurostat developed for the early GDP estimates and discusses

the user needs motivating the advancement of GDP estimates. At the core of the methodology Eurostat uses a

sample to population estimator in which the sample is formed by the GDP t+30 estimates of a group of

Member States. The paper also discusses a possibility to top-up the sample to population estimate by means of

the economic sentiment indicator, particularly in case of a difficult rounding situation (~ x.x5 % growth) for a

publication growth rate with one decimal point. Furthermore, the paper analyses the results of the estimates for

16 test quarters that are based on the national estimates of a group of Member States and that were prepared in

close cooperation with them. Finally, the article discusses the a priori set quality acceptance criteria for the test

estimates, assesses the test results against those criteria, and concludes that the test results passed all

predefined quality criteria.

JEL Codes: C82, E01, E32

Keywords: Gross domestic product, economic growth, early estimates, monitoring economic growth and

business cycle

1. Introduction

The research question addressed in this article is the following: Estimating reliably European GDP at 30 days

after the quarter-end – is that feasible?

Since 2003, the first quarterly GDP estimates for the euro area and the EU have been produced at 45 days after

the quarter-end. In comparison, one of the main EU trading partners, the US, compiles its first quarterly GDP

estimate at 30 days since the late 1970s. Some European countries – United Kingdom, Spain, Belgium,

Lithuania and more recently Austria, Latvia and France – publish GDP flash estimates at 30 days after the

quarter-end as well.

Eurostat started to investigate the possibility of advancing the first GDP estimate for the euro area and the EU

with a group of Member States in 2013. The article discusses whether and how Eurostat, in close cooperation

with Member States, has met the challenge of the above research question.

Eurostat began publishing quarterly GDP flash estimates in 2003. Since then, these estimates have been

released every quarter, 45 days after the quarter-end. The introduction of the GDP t+45 flash estimates was

described in the Eurostat flash project (Eurostat, 2003) as the project’s ‘first practical objective’. Reducing the

time needed to produce a flash estimate of GDP to 30 days was cited as a ‘next step’ for the project. Ten years

later, in May 2013, a task force was established with the mandate of assessing whether it would be possible to

publish a sufficiently reliable flash estimate of GDP for the euro area and the EU based on the information

available at t+30 days, including national estimates produced by the Member States.

The work on the GDP t+30 days project covered:

sharing information on and best practices for preparing early quarterly GDP estimates between Member

States;

producing a country-by-country overview of the sources available for GDP estimates between t+25 and

t+60 days;

developing a guidance document on methods and national estimation techniques;

developing a method for producing GDP t+30 flash estimates for the euro area and the EU;

developing quality acceptance criteria to be used for assessing the test results;

preparing test estimates; and

developing a communication plan.

The paper is organised as follows: Section 2 discusses the question of why the GDP t+30 flash estimates for

the euro area and the EU are being introduced and elaborates user needs. Section 3 examines the estimation

methodology developed by Eurostat. This methodology was used for preparing the test estimates and will

continue to be used for producing the official estimates. The methodology for GDP t+30 is placed in a broader

perspective by also addressing the methods used for the GDP t+45 and the ‘regular’ annual and quarterly

national accounts estimates. Section 4 discusses the quality acceptance criteria and how they were developed

for assessing the results of the test estimates. Section 5 presents the results of the 16 quarterly test estimates,

and the assessment of these results against the quality acceptance criteria. The test estimates are also compared

with the US results for the corresponding quarters. Section 6 concludes the article.

2. Why introduce GDP t+30 estimations?

2.1 Introduction, user needs and developments in official statistics

The question as to why GDP t+30 flash estimations are being introduced can be answered by considering three

issues: user needs and developments in official statistics, the background of the GDP t+45 flash estimates, and

the link between the GDP estimates and the Principal European Economic Indicators (PEEIs).

User needs, economic and financial developments and technological improvements inevitably trigger changes

and further progress in the area of official statistics. In view of this, users’ demand for more detailed

information and for information to be available sooner plays an important role.

At a strategic level, in the ESS Vision 2020 the European Statistical System (ESS) has committed to ‘respond

to the need to provide policymakers with reliable, comparable and timely statistics to execute economic and

financial policy’ (European Statistical System (ESS), 2013). The work on the GDP t+30 flash estimates is one

aspect of the action being taken by the ESS to fulfil this commitment.

Since May 2003, Eurostat has been publishing a flash estimate of quarterly seasonally and calendar-adjusted

GDP growth 45 days after the end of the reference quarter (t+45). This has been greatly appreciated by the

users of statistics and in particular by policymaking organisations such as the European Commission and the

European Central Bank (ECB). The economic, financial and technological developments seen in recent years

mean, however, that policymakers increasingly need to analyse economic activity faster, i.e. sooner after the

end of a reference period. Sooner available high quality, reliable published statistical data is therefore

essential. As a result, policymakers and other main users of statistics were keen to see quarterly GDP estimates

available earlier.

Main users: the European Commission and the European Central Bank

The European Commission’s Directorate-General for Economic and Financial Affairs (DG ECFIN) and the

ECB rely heavily on the macroeconomic statistics produced and disseminated by Eurostat, and in particular on

the quarterly national accounts. They therefore supported the ESS’s work on producing GDP t+30 flash

estimates for the euro area and EU. Bringing the GDP release date forward is seen as a significant

improvement in data availability, and it also meets users’ long-standing demand to have flash estimates

available for the euro area and the EU at a similar date to that at which data is available for the other main

economies, and in particular the euro area’s main trading partners, such as the United States and the United

Kingdom.

Having GDP estimates available earlier will be useful for the following purposes:

A. For policy decision-making

The ECB is responsible for monetary policy in the euro area. The ECB’s Governing Council aims to keep

inflation below, but close to, 2% over the medium term. In order to achieve this objective, the Governing

Council bases its decisions on a two-pillar monetary policy strategy, and implements them via its operational

framework. The two pillars are economic analysis and monetary analysis — these form the basis of the

Governing Council’s overall assessment of the risks to price stability, and thus of its decisions on monetary

policy. The ECB’s economic analysis focuses on real economic activity, and therefore takes into account the

fact that price developments over those horizons are largely determined by the interplay of supply and demand

in the goods, services and factor markets. The GDP flash estimate is thus one of the most important indicators

used when setting monetary policy, in particular because policy decisions influence developments in economic

variables such as output and prices. Bringing the quarterly GDP flash estimate forward by two weeks is

therefore valuable to the ECB for its monetary policy decision-making.

B. For monitoring the economic situation

DG ECFIN provides a continuously updated assessment of the overall economic situation in the euro

area and in the EU. This is used in discussions by all groups and committees working in areas covered

by DG ECFIN, including particularly the Eurogroup. DG ECFIN and other Commission departments

are also in close and frequent contact with other international organisations.

The ECB (specifically the Directorate General Economics) produces updated assessments of the overall

economic and monetary situation in the euro area and briefing notes that include the latest statistics on a

regular basis. These are then used by the ECB’s Executive Board and its Governing Council to inform

their discussions, and by other EU bodies and international fora.

Having a sound understanding of the current developments in the economy, at an aggregate level, is critical in

the contexts mentioned above. This understanding is informed by all the available statistics and indicators, and

earlier availability of GDP estimates would therefore be of great benefit, GDP being the standard accepted

aggregate measure of economic activity.

A reliable, objective and publicly available measure, such as GDP growth in the euro area and the EU, can

help to establish a common understanding in international fora, and having this information available earlier

would therefore be very valuable in this context also.

C. For forecasting/projection purposes

The Commission’s macroeconomic forecasts for the euro area and the EU are built bottom-up by

aggregating data from individual country forecasts produced by country desk officers in DG ECFIN,

but also include top-down elements, such as information provided by European aggregates. These

forecasts are produced three times a year (winter, spring and autumn) and each forecast involves several

iterations. Estimates of GDP for the euro area and the EU released 30 days after the end of the reference

period could be of great value for forecasting. At least in the current forecast set-up, the flash estimate

at t+30 days would still be released after the internal ‘cut-off date’ for information for each of the three

forecasts, and could not therefore be taken into account when producing the forecasts. Nonetheless, in

contrast to the t+45 releases, these estimates would be available prior to the publication of the forecast

(the Q4 estimate would be available before the publication of the winter forecast in early February, the

Q1 estimate before the publication of the spring forecast in early May, the Q3 estimate before the

publication of the autumn forecast in early November). This would enable the communication issued at

the time of the forecast release to be adapted to the latest economic developments.

Whether the earlier availability of the European aggregates could help to ensure and improve the quality of the

forecast in future depends on when a t+30 days release would fall in future forecast calendars. If the GDP

estimate were available at an early stage in the forecasting calendar, it could help to shape the central guidance

issued to country desks at the beginning of the forecast exercise. This would thus ensure that national forecasts

reflected the available aggregated figures (top-down approach) and that country forecasts were produced on

the basis of a common interpretation of the current economic situation. If available at a later stage of a forecast

exercise, the GDP t+30 flash estimates could be used for checking the plausibility of the aggregated national

forecasts.

The ECB carries out a number of forecasting and projection exercises as part of its monetary policy

strategy. Two distinct types of projections can be identified.

The first are the forecasted ‘early’ estimates of quarterly GDP growth, which are produced twice a

month. The forecasting model is a complex tool that combines backcasting and nowcasting techniques,

focusing on quarterly developments. The earlier availability of a GDP flash estimate for the euro area

will be quite significant for this type of forecasting. Having the GDP estimate available sooner would

also reduce the time-gap between the release of this and other economic indicators used in the

forecasting process.

The second type of forecasting is the macro-projection exercise, which is performed on a quarterly

basis in two streams (one of which also involves all EU national central banks) and is similar to the

forecasting carried out by DG ECFIN. The results of the ECB’s macro-projections are made publicly

available to users via the ECB’s website and are also discussed in a dedicated publication. There is a

‘cut-off’ date for data to be included in these projections and it is important both for euro-area

aggregates, such as GDP, and for the euro-area and EU Member States individually, that all statistics

are taken into account and that the most recent data are included. Bringing the flash estimate of GDP

for the euro area and the EU forward is therefore also useful for this type of projection.

Other users

In addition to the main users discussed here, there are also many other users who will benefit from data on

GDP growth being available sooner. These include other Commission departments, such as the Directorate-

General for Employment, Social Affairs and Inclusion and the Directorate-General for Financial Stability,

Financial Services and Capital Markets Union. In addition, having GDP data available earlier will be of

relevance for institutional users such as the European Council and the European Parliament. Earlier

information on the GDP growth rate in the euro area and in the EU will also be useful for national

policymakers and governments. Finally, the general public is better served by providing earlier, but still

reliable estimates of economic development.

2.2 Background to the GDP t+45 days estimates

The aim of the GDP t+45 estimates was (and still is) to provide quarter-on-quarter and year-on-year seasonally

and calendar adjusted growth rates for quarterly GDP. Results for the euro area, the EU and for individual

Member States that publish data at a national level are published in Eurostat’s news release at (or slightly

before) 45 days after the end of the reference quarter.

Eurostat started producing and releasing the t+45 GDP estimates in 2003. At the time, the euro area and the

EU comprised, respectively, 12 and 15 countries. At the beginning of the project, five countries (Germany,

Greece, Italy, the Netherlands and the United Kingdom) provided their national estimates to Eurostat. These

countries together accounted for more than 50% of the EU GDP. For the large Member States that could not

provide national estimates, related indicators were used. The national estimates (for the countries listed) and

related indicators (for other large countries) provided the input for a regression model that estimated the GDP

for the euro area and the EU. The launch of the GDP t+45 releases in 2003 was viewed as an intermediate

stage that would eventually lead to estimates of quarterly GDP being released 30 days after the end of the

reference quarter.

Gradually, more Member States started producing estimates of national GDP at t+45 days. By 2006Q1, for

example, the countries contributing to the GDP flash project represented 74% and 72% respectively of the

euro-area and the EU GDP. By 2015Q2, this had risen to 97% for the euro area and 95% for the EU. The

revisions made to the GDP t+45 estimates at the first regular release at t+65 days are very small. The estimates

of the European aggregates are now almost entirely based on Member States’ input. Estimation techniques and

modelling are no longer used. Sub-section 3.2 discusses the methodology used to produce the GDP t+45

estimates for the euro area and the EU in more detail. Table 1 in Sub-section 4.3 describes in turn the good

revision performance of the euro area t+45 estimates.

2.3 Link with Principal European Economic Indicators (PEEIs)

Users of EU economic statistics have, for a long time, been looking forward to see releases of European

national accounts data set to a calendar of 30, 60 and 90 days after the end of the reference period. This would

match the established practices for data releases of other critical monthly and quarterly macroeconomic

indicators as well as those of the EU main economic partners such as the United States. The largest euro area

and EU Member States are also already following this schedule for data releases.

A first attempt at assessing the feasibility of compiling a GDP t+30 flash estimate for the euro area and the EU

was made in 2008, as part of a work on the Principal European Economic Indicators (PEEIs), which includes

the GDP flash estimate. In a workshop organised by the ECB Directorate General Statistics, the practices of a

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number of national statistical institutes, the users’ needs of ECB’s statistics, and the Eurostat plan to develop

GDP t+30 flash estimates for the euro area and the EU were discussed. The schedule for data releases

proposed as a result of this initiative was as follows:

30 days: advanced estimates (‘flash estimates’) of GDP, possibly employment, and ideally some

expenditure/output components;

60 days: preliminary estimates of GDP and the main expenditure and output components; a flash

estimate of the balance of payments;

90 days: comprehensive quarterly data estimates of GDP and main expenditure and output components,

plus quarterly financial and non-financial accounts for institutional sectors and balance of payments

statistics.

Although this proposal was not put into practice at the time, the users’ and policymakers’ need for earlier

estimates remained the same.

The main advantage of the proposed schedule, with data releases at 30, 60 and 90 days was (and still is) that it

allows a comprehensive and consistent approach to be taken to data releases across the different areas within

national accounts. The proposed GDP t+30 flash estimates are an important part of this schedule of releases.

3. Eurostat’s estimation methods

This section discusses the method used by Eurostat for compiling the GDP t+30 flash estimates for the euro

area and the EU. This method was developed by Eurostat and used to produce the test estimates and it is used

to compile the regular GDP t+30 estimates that are released as of the 1st quarter 2016.

Sub-section 3.1 introduces the terminology related to flash estimates. Sub-section 3.2 discusses first the overall

methods used for preparing the annual and quarterly national accounts. As the method for preparing the GDP

t+30 flash estimate was designed to be as close as possible to that used for the GDP t+45 flash estimate, Sub-

section 3.2 elaborates secondly the method used to compile this latter estimate. Finally, the sub-section

concludes by presenting the method developed for the GDP t+30 estimates.

3.1 Flash estimate for a quarterly national accounts variable: terminology

The users of national accounts data have been calling for reliable, early quarterly European national accounts

figures for some time. The short-term indicators currently available (e.g. production and other short term

statistics indices, statistics on prices and foreign trade and business surveys) help users to form a picture of

economic developments in a particular variable and/or industrial activity. In order to obtain a more complete

picture of developments at macroeconomic level, however, there needs to be a system in which each partial

variable can be assessed with respect to other variables, and in which the breakdown of a variable is shown as

proportions of an aggregate figure.

Quarterly national accounts form such a system. Users would like to have at their disposal preliminary flash

estimates available for all the main quarterly national accounts variables. Ideally, all the variables would be

published soon after the end of the quarter and would be reliable. Experience has, however, shown that it is

easier to produce a reasonably reliable early estimate of aggregate GDP than of its components. On top of that,

quarterly GDP growth is the headline indicator of the quarterly national accounts.

The flash estimate of quarterly GDP:

gives an early picture of economic development;

can be used in conjunction with other national accounts variables;

is produced and published as soon as possible after the end of the quarter; and

is based on a less complete set of information than is the GDP estimate given in the traditional quarterly

national accounts.

Flash estimates differ equally from forecasts, pure nowcasts and leading indicators. The aim of producing GDP

flash estimates at EU level is to estimate GDP growth in a way that is, as far as possible, similar to that in

which later regular estimates are produced but by using less complete data sources.

Flash estimates and traditional estimates of quarterly accounts differ in a number of their characteristics:

Release date: flash estimates are available earlier than traditional estimates (typically within 30-45

days).

Accuracy: there is a trade-off between timeliness and accuracy. Flash estimates are in general less

accurate than traditional estimates. The loss of accuracy is, however, kept as small as possible. (2)

Reference period: flash estimates are typically only produced for the latest quarter. The data for the

preceding and earlier quarters are not usually revised.

Coverage: the number of breakdowns of variables included in flash estimates is usually more limited.

Information available: flash estimates are based on a more limited set of information. Information from

surveys covering the whole quarter, for example, is often not available.

(2) For more discussion on timeliness and accuracy, see e.g. Fixler, 2007.

Use of estimates: due to the lack of direct information, flash estimates may include components that are

estimated using statistical methods. For example, there may be only two months of short-term statistics

available. Other available related indicators might thus be used for the third month. The third month

estimate, included in the flash, would typically be produced by combining all the back information on

past observations with a current quarterly indicator by using autoregressive distributed lag (ADL)

models (see e.g. Stock & Watson, 2007), autoregressive integrated moving average with exogenous

variables (ARIMAX) models and time series regression techniques. (On ARIMA and ARIMAX models

and time series regression techniques, see e.g. Box & Jenkins, 1976; Hamilton, 1994; Brockwell &

Davis, 2003; Eurostat, 2016b.)

3.2. Compilation methodology

The European Statistical System (ESS) is a network formed by the national statistical institutes in the Member

States, plus Eurostat, the European Commission’s statistical office. The national accounts figures for the euro

area and the EU are compiled by Eurostat using the national accounts figures submitted by the Member States’

national statistical institutes. Therefore, the European aggregates, despite being calculated by Eurostat, also

depend on input from the whole ESS.

Regarding the national accounts main aggregates, the same approach is used for data on all variables,

irrespective of the timing. This goes from the supply and use tables, sent 36 months after the end of the

reference period, and which include the most detailed breakdowns, to the quarterly GDP flash estimates, sent

45 days after the quarter-end. The national accounts data sent by Member States are based on primary

statistical data gathered by each of the national statistical institutes. The European aggregates are therefore

produced using an indirect approach, i.e. on the basis of data gathered at Member State level, rather than by

surveying the variables directly at EU level.

Compilation of annual and quarterly European national accounts

The European System of Accounts 2010 (ESA2010) provides guidance with the aim of achieving consistency

across Member States’ national accounts data. Country data need to be comparable in order to be suitable for

compiling European national accounts. The ESA2010 transmission programme is included as an Annex to the

ESA2010 Regulation (Eurostat, 2013). The programme sets out the deadlines for submitting national data to

Eurostat. Eurostat thus receives the required data from most Member States. Its first step in producing the

European annual national accounts is to aggregate the national data to give the totals for the euro area and the

EU. This first aggregation is done in current prices, and is thus a simple addition, as data in current prices are

additive. To the contrary, the national figures for chain-linked volumes with moving base years are not

additive. Therefore, the country data have to be totalled in the previous year’s prices to obtain the aggregate

variables for the euro area and the EU. Calculating the chain-linked volume figures for the European aggregate

variables in year t requires both of the following to be available: figures for the European aggregate variables

for year t in the previous year’s prices, and figures for year t–1 in current prices. Furthermore, after having

carried out the first figures aggregation, the European-level national accounts data in current and previous

year's prices have to be balanced, so that, e.g. the components of (final) supply and (final) use components will

add up to the same figure.

For the quarterly national accounts data transmissions, for example at 60 days after the quarter-end, some

Member States have derogations allowing them to send data later than specified in the requirements. Data for

the vast majority of, but not all, Member States are therefore available for compiling the European quarterly

national accounts. As a result, the quarterly European level figures (in current prices and in chain-linked

volumes) cannot be directly calculated due to missing data for certain countries. To solve this problem, another

indirect approach is applied using the time dimension: the annual European national accounts level figures are

temporally distributed to the quarters based on the quarterly national accounts figures of those Member States

that sent quarterly data to Eurostat. The temporal disaggregation of the annual figures is performed using the

Chow-Lin regression-based method (Chow & Lin, 1971). A linear model is specified to describe the

relationship of the quarterly GDP indicator with the annual GDP. This model can also be used for estimating

quarterly changes in GDP for the most recent quarter(s) for which annual GDP is not available. The process of

disaggregating the annual total over time also ensures that the quarterly figures add up to the annual ones: the

non-adjusted quarterly figures add up to the non-adjusted annual figure, and the seasonally and calendar-

adjusted quarterly figures add up to the calendar-adjusted annual figures.

Method for producing the GDP t+45 flash estimate

The ESA2010 transmission programme requires Member States to send the first set of quarterly national

accounts data two months after the end of the quarter. In view of users’ need to have data on GDP available

earlier than this, the majority of Member States have also agreed to provide a flash estimate of quarterly GDP

to be used for compiling the GDP t+45 flash estimates for the euro area and the EU. In most cases, Member

States and Eurostat currently publish their GDP t+45 estimates on the same day.

Given that 45 days after the quarter-end is a relatively short deadline for producing macroeconomic statistics,

it was agreed when Member States first started providing the GDP t+45 estimates that they would only be

expected to transmit the seasonally and calendar-adjusted GDP growth rates. The growth figures they send are:

i) the reference quarter compared with the previous quarter (quarter-on-quarter growth); and ii) the reference

quarter compared with the same quarter of the previous year (year-on-year growth). Providing information on

the seasonally adjusted quarter-on-quarter growth (including calendar adjustment where relevant) was seen as

the main target of the GDP t+45 flash estimates. Whenever these data are available for a Member State,

Eurostat therefore uses the quarter-on-quarter national GDP growth as its primary information.

The GDP t+45 flash estimates for the euro area and the EU have been published since 2003Q1. Eurostat

developed the method for producing the flash estimate and tested its performance before the first data release.

The GDP t+30 flash estimate has been developed following a similar procedure, and the aim was to make the

methodology for producing this estimate as similar as possible to that already being used for the GDP t+45

flash estimate. It is therefore useful to consider briefly the methodological decisions that were taken during the

development of the GDP t+45 flash estimates.

The first regular GDP t+45 flash estimate for the euro area and the EU was already being prepared at that time

using the Chow-Lin regression-based temporal disaggregation technique, in a manner similar to that described

above. To calculate an estimate of GDP for the most recent quarter(s), the specified Chow-Lin regression

model relation between quarterly GDP indicator (deviating from the annual level) and annual GDP was

applied for obtaining a European quarterly GDP that is in line with the evolution at annual level.

During the testing phase of the GDP t+45 estimates for the euro area and the EU, there were five Member

States producing GDP estimates before or at t+45 days: Germany (t+45), Greece (t+45), Italy (t+45), the

Netherlands (t+45) and the United Kingdom (t+25). For two other large economies (France and Spain) for

which GDP t+45 estimates were not yet available, the industrial production index of the reference quarter was

available before t+45. For these two countries, GDP growth was therefore estimated using a regular regression

model for which the inputs were one or more available indicators (typically including the industrial production

index).

Next, the temporal disaggregation was prepared for quarters up to the quarter preceding the reference quarter

(Q-1):

1. by aggregating the annual GDP of all countries up to the most recent year available; and

2. by aggregating the quarterly GDP of all countries on which it was available for quarters up to Q-1

(GDP data for Ireland and Luxembourg were missing at that time).

In order to complete the quarterly GDP indicator time series, i.e. to have a figure for the GDP indicator for the

reference quarter (Q), the weighted average (3) of the quarterly growth rates of the countries providing flash

estimates was considered as the growth estimate for the EU (for which there were seven such countries) and

for the euro area (for which there were six country estimates). The quarterly GDP indicator series (as described

(3) The proportions of Member States' current price GDP (in euro) in the EU GDP and euro area GDP were used as weights.

in point 2 above) was then extended to include the reference quarter Q by applying the calculated estimates of

the euro area and EU growth rates to the series.

It should be remembered that the quarterly indicator series (referred to in point 2 above) was not at the same

level as the annual series due to quarterly GDP data being missing for two countries. As a last step, temporal

disaggregation was therefore applied using the Chow-Lin regression model, to align the annual and quarterly

GDP series.

The method for producing the GDP t+45 flash estimates described in this section was mainly used until 2013,

at which time the methodology was simplified. Since 2013, the quarterly GDP levels for the euro area and the

EU have been directly derived by applying the respective quarter-on-quarter growth rates for quarter Q to the

GDP levels for quarter Q-1. These growth rates are obtained by aggregating the countries’ GDP t+45 flash

growth rates using the weights of their GDP in current price euros for year y-1. The main factors that made this

simplification possible were, first, that countries that had not been providing quarterly GDP data in 2003 had

started to do so, and second, that by 2013, the number of Member States producing GDP t+45 flash estimates

had grown such that they then accounted for over 90% of euro-area and EU GDP (4).

The GDP t+45 flash

estimates for the euro area and the EU are therefore now almost entirely based on the input from Member

States, with estimation techniques and modelling no longer being used.

Method for producing the GDP t+30 flash estimate

When the GDP t+30 project started its work in May 2013, four Member States — Belgium, Lithuania, Spain

and the United Kingdom — were already publishing a GDP flash estimate at t+30 days or earlier (the UK

publishes at t+25 days). The aim was to document the experience and best practices learnt by Member States

that already publish a flash estimate at t+30 days, those that are testing or have tested its feasibility and those

who would be willing to start testing the possibility. Another, more specific objective of the project was to

assess whether it would be possible to publish a sufficiently reliable flash estimate of GDP for the euro area

and the EU, based on the information available at t+30 days and including national estimates produced by the

Member States. (5) It should, however, be emphasised that the project did not aim to push Member States to

publish national quarterly GDP data at t+30. The decision as to whether or when to publish data is left entirely

to the national statistical institutes.

The choice to use an indirect approach had already been made at the beginning of the project, and before

starting to produce the GDP t+30 test estimates for the euro area and the EU. The flash estimates produced by

Member States, whether published or not for internal use only, and/or the indicators available at t+29, are

therefore used as the main data sources, rather than indicators at euro area or EU level. The exact definition of

the statistics to be provided for the GDP t+30 estimates is the same as that for the GDP t+45 estimates:

seasonally and calendar-adjusted quarter-on-quarter and year-on-year growth estimates for the euro area and

for the EU. When developing the method by which to produce the GDP t+30 flash estimate, the approach

taken was therefore to follow the method already being used for the GDP t+45 flash estimates as closely as

possible.

The process for producing the GDP t+30 flash estimates for the euro area and the EU can be presented as five

steps:

A group of Member States send their t+30 quarter-on-quarter and year-on-year seasonally and calendar-

adjusted GDP growth estimates 29 days after the end of the reference quarter. This group includes

Member States that already publish their t+30 estimates (6) and Member States that send confidential

estimates to Eurostat.

(4) For the t+45 flash estimates for 2013Q1, for example, these Member States accounted for 97% of euro-area GDP and 95% of EU GDP. In September

2015, five Member States did not provide GDP t+45 estimates: Croatia, Denmark, Malta, Slovenia and Sweden. Sweden only provides a GDP t+30 estimate for the second quarter.

(5) More information on Member States’ estimation methods particularly concerning missing data for t+30 estimates can be found in Eurostat Statistical Working Paper “Overview of GDP flash estimation methods” (Eurostat, 2016b).

(6) By the end of 2015, six Member States were publishing quarterly GDP estimates before or at t+30: Austria, Belgium, Latvia, Lithuania, Spain and the United Kingdom. In addition, France began to publish its GDP t+30 estimate in January 2016.

Eurostat aggregates the countries’ quarter-on-quarter growth rates using the weights of their respective

annual GDP in current price euros for year y-1, to produce aggregate growth rates for the euro area and

the EU. (See equation A.5 in Annex A for further details. Annex A also provides a more extensive

discussion on the method used for aggregating the volume growth rates of the components of GDP.)

Optional step: estimating the growth rate for a major EU country in case such country data are missing.

If the GDP estimate for a major Member State is not available, its GDP growth is estimated using other

available data. The other available data would typically consist of indicators such as the industrial

production index, deflated retail trade and the turnover of services, for which two months’ data would

be available and the third month could be nowcast. Rather than relying only on a one-point estimate, the

aim is to have a number of nowcast estimates, in order to be able to compare them. Nowcast estimates

of national data would typically be produced in the following ways:

1. using the national accounts weights of the country to weight the growth rates of the industrial

production index, deflated retail trade and turnover of services;

2. using all or some of the indicators mentioned above in an ADL or ARIMAX model, together

with the GDP;

3. using the economic sentiment indicator (ESI) in one of the models mentioned in point 2. (7)

The above estimates can then be compared with forecasts issued by official and/or commercial

forecasters. Once an estimate has been determined for a country for which data were missing, it can

then be included in the aggregation of the country growth rates, along with the other GDP estimates

provided directly by the Member States.

Optional step: using the economic sentiment indicator to top-up the European estimate in a difficult

rounding case. If there is a situation where rounding poses a potential problem, i.e. if the second

decimal of the GDP t+30 estimate for either the euro area or the EU is close to 5 (i.e. a growth rate of ~

x.x5%), this estimate can be topped up by using the ESI for the part of the European aggregate for

which country estimates are missing. A weighted aggregate of the ESIs of the countries for which GDP

estimates are missing would be calculated. This would then be entered into an ARIMAX model,

together with the aggregated GDP growth rate for previous quarters for the same set of countries, in

order to nowcast the development of the reference quarter. In the most recent test estimates, Member

States that were not providing GDP flash estimates accounted for approximately 10% of EU GDP and

6% of euro-area GDP. The contribution of these countries to the developments seen at euro-area and

EU level is therefore typically minor. More extensive information about how ESI can be used is given

below in a separate sub-section.

Once a final quarter-on-quarter GDP growth estimate has been obtained for the euro area and the EU,

the GDP level estimates in chain-linked volumes for both areas for the reference quarter (Q) are then

derived by applying the quarter-on-quarter GDP growth rate to the seasonally and calendar-adjusted

GDP figures for quarter Q-1. The seasonally and calendar-adjusted estimate of GDP in the reference

quarter (Q) is used to calculate an estimate of the year-on-year GDP growth for both the euro area and

the EU.

Top-up of the t+30 growth estimates with the economic sentiment indicator

As described above, the core of the Eurostat GDP t+30 flash estimates is based on a sample to population

estimator. The growth rates of those Member States providing estimates are weighted together to form an

estimate for the euro area and the EU. In the last test estimate (for 2015Q4) the coverage of these 17 countries

formed 90.6% of the EU28 GDP in the previous year; the euro area countries (11) in this group covered 94.3%

of the EA19 GDP, respectively. This section discusses in more detail, whether the development of the GDP for

the missing part, the 'residual' GDP growth, could be estimated with existing economic sentiment indicator

(7) The European Commission Economic Sentiment Indicator (ESI) is a leading indicator that combines consumer confidence and business confidence

indicators of European countries (European Commission, 2016). Economic sentiment indicator values are freely available for the European countries, for the euro area and European Union in Eurostat data base: http://ec.europa.eu/eurostat/data/database?node_code=ei_bssi_m_r2

.

(ESI). As given above, the top-up procedure discussed below may be used when the sample to population

estimator gives a value in which the (up or down) rounding to one decimal growth rate is on the border (i.e. a

growth rate of ~ x.x5%). We use the top-up of the sample to population estimator for the EU here as an

example, but the same procedure applies for the EA19 as well.

In order to be able to achieve the goal, we need to divide the EU Member States into two groups. The first

group, named 'exogenous' group, includes the countries already providing their estimates. The second group,

named 'endogenous' group, contains the countries (9 for 2015Q4) for which estimates are missing, i.e. the

'residual' GDP growth of the EU28 not yet estimated. To test whether we could estimate the 'residual' GDP

growth, the GDPs and the ESIs were aggregated both for the exogenous and endogenous group from 2003Q1

onwards.

The rationale why ESI could be used to estimate the 'residual' GDP after the sample to population estimate

(exogenous group), is given in Figure 3 of Annex D. The figure plots the seasonally adjusted year-on-year

GDP growth rates for the EU28, the endogenous group and the exogenous group together with the seasonally

adjusted ESI index points of the same economic areas. The highest correlation with the seasonally adjusted

ESI is found with the year-on-year GDP growth of the EU (correlation coefficient for the EU rEU = 0.93 and

for the euro area rEA = 0.94 with data for 2003Q1–2015Q4), and therefore the year-on-year seasonally adjusted

GDP growth of the endogenous group is estimated.

The top-up of the t+30 estimate with ESI for the EU is performed in three steps:

1. The lacking year-on-year growth rate of the last quarter for the 'residual' (or endogenous group's) GDP is

estimated by using an AR(I)MAX model with aggregated national ESI used as the exogenous input. (8)

The basis for the use of the AR(I)MAX model is given by the fact that both GDP growth and the ESI time

series were tested to be stationary. In addition, the AR(I)MAX model proved to provide best nowcasts for

the 'residual' GDP. The model has the following structure: 'residual' year-on-year GDP growth is regressed

with the ESI of the endogenous ('residual') group together with autoregressive and/or moving average

term. The number of lagged autoregressive and/or moving average terms is identified by using Bayesian

(BIC, also known as Schwarz's information criteria) and Akaike’s (AIC) information criteria. (9)

Alternative 'residual' GDP growth estimates for the last quarter are produced by using the ESI of the

residual group, the ESI of the whole EU or the ESI of the exogenous group as the exogenous input. The

final estimate for the 'residual' GDP may be an average of three to five different model estimates. An

example of a specified model is given in Table 10 and Figure 4 of the Annex D.

2. The previously received sample to population year-on-year growth estimate (exogenous group) and the

year-on-year growth rate estimate for the 'residual' (endogenous group) is weighed together. For 2015Q4

the weights are 90.6% and 9.4%.

3. The year-on-year GDP growth rate for the whole EU28 is applied to the GDP level of the same quarter a

year ago for obtaining a level estimate for the quarter. The quarter-on-quarter GDP growth estimate for the

EU28 is then to be calculated between the GDP level figures of the two last quarters.

(8) On ARIMAX models, see e.g. Box & Jenkins, 1976; Hamilton, 1994; Brockwell & Davis, 2003.

(9) The basic principle in both information criteria is that one aims to choose a model with as small residual variance as possible with as little as possible number of model parameters. The model with the lowest information criteria value is chosen. See e.g. Akaike, 1973; Schwarz, 1978; Brockwell & Davis, 2003; Stock & Watson, 2007.

4. Quality acceptance criteria

4.1 Introduction

An important part of the GDP t+30 project was to assess the feasibility of producing a flash estimate of GDP

growth at 30 days after the end of the reference quarter for both the euro area and the EU (10

). The EU Member

States that participated in the project were therefore asked to provide test data in real time from 2014Q1 to

2015Q4 (with delivery of the data no later than 29 days after the end of the quarter). In addition, data were to

be ‘reconstructed’ for all quarters going back to 2012Q1. Member States that were already producing GDP

flash estimates at t+30 were able to simply supply Eurostat with these estimates. The countries that were not

already producing GDP flash estimates at t+30 days were asked to calculate their national estimate

retrospectively (i.e. using the data that would have been available to them 29 days after the end of the quarter).

National data were therefore available for 16 quarters (eight quarters in real time and eight quarters as a

mixture of retrospective and real time results) in order to test the quality of the GDP t+30 flash estimates

produced for the euro area and the EU.

In order to assess the feasibility of producing a flash estimate of GDP growth in the euro area and the EU at 30

days after the end of the reference quarter, it was necessary to set a series of criteria that would have to be

fulfilled by the results obtained by the test estimates. These ‘quality acceptance criteria’ and how they were

determined is the subject of this section.

Sub-section 4.2 examines the definition of quality. Sub-section 4.3 discusses some of the considerations that

were taken into account when setting the quality criteria. Sub-section 4.4 presents the criteria to be used for

assessing the quality of the test estimates.

4.2 Defining quality

Quality is a term frequently used in statistics, but its definition may vary. It can be defined in a narrow or in a

broader way. In the former case, the focus is purely on statistical accuracy. In the latter, the definition may also

include accessibility and timeliness, i.e. how soon statistics are released after a reference period. It is clear that

quality is important to users of official statistics and that it should be a main consideration when developing

statistics for publication.

The ESS recommends that quality assessment of statistics should be based on nine areas:

relevance, assessment of user needs and perceptions;

accuracy and reliability;

timeliness and punctuality;

coherence and comparability;

accessibility and clarity;

cost and burden;

confidentiality;

statistical processing.

These different aspects of quality should all be considered when developing statistics for publication. For the

GDP t+30 flash estimate, however, at least in the early stages of development, the main considerations were

accuracy and timeliness. These two dimensions are discussed in more details below.

The accuracy of the GDP t+30 flash estimate is probably the most important quality indicator. The aim is to

produce an estimate that gives a good indication of GDP growth but at an earlier point in time than the current

(10) In 2016, the EU is made up of 28 Member States, 19 of which are in the euro area. The test estimates for the period 2012-2015 were carried out using

the ‘changing composition’ of the euro area and the EU, i.e. on the basis of the countries actually in the euro area and the EU at any particular point in time. The test estimates for the EU produced between 2012Q1 and 2013Q2 therefore relate to 27 Member States, whilst those for later quarters are based on 28 Member States. The number of euro area countries was 17 in 2012/2013, 18 in 2014 and 19 in 2015.

GDP t+45 estimate. The quality of later estimates is assessed regularly. A ‘good’ GDP t+30 flash estimate is

therefore one that consistently produces an estimate of growth ‘similar’ to the ones released later (at t+45, t+65

and a later estimate such as t+100 or the estimate for current quarter when the regular t+65 estimate is

published for the next quarter, i.e. at t + 3 months + 65 days (11

)). The revisions needed to the GDP t+30 flash

estimates will form the basis of one of the acceptance criteria.

It may also be of interest to examine the revisions needed for individual Member States’ GDP flash estimates.

However, assessing the quality of the Member States’ estimates goes beyond the scope of this paper. The only

revisions considered for developing the quality acceptance criteria will be those needed for the GDP t+30 flash

estimates for the euro area and the EU. (12

)

The timeliness – the time between the end of the reference period and the publication – is set in the case of the

GDP t+30 flash estimates by definition. It is important to ensure that the EU Member States involved

consistently send their data by the t+29 deadline (13

) in order to avoid any risk of the European aggregates

publication being delayed.

4.3 Considerations when setting the acceptance criteria

A number of issues had to be considered before setting the quality acceptance criteria. One critical

consideration was to determine if enough observations would be available to identify whether the aggregate

has a sufficient quality. Using retrospective back data from Member States enabled to extend the time series

but they still amount to 16 quarters of data only. Such short time span will obviously increase the risk in

results’ quality giving a misleading picture of the statistics’ accuracy and thus an incorrect assessment.

The data for quarters from 2012Q1 to 2013Q4 were, for the majority of Member States, produced on a

retrospective basis. During initial discussions about the possible methods for producing flash estimates, a

number of Member States indicated that their normal methods were not entirely theoretical, and that expert

judgement also played a role. Retrospective data can only be produced using a purely theoretical approach,

which may potentially lead to inferior results compared to those that would have been produced had there been

an element of expert judgment (although there is no way to prove this). Consideration should also be given to

the fact that Member States are at the start of a process of development. It would be expected that Member

States will refine their methods during the next two years, leading to a gradual improvement in results.

Accordingly, later quarters may provide a better barometer for accuracy than the earlier estimates. This,

however, is very much dependent on the Member States’ approach to developing their methodology for flash

estimates.

As stated in the previous section, the preferred measure of accuracy is the revision made to the GDP t+30 flash

estimate. A useful starting point for determining what is an acceptable level of revision is to consider the

revisions made to the current GDP t+45 flash estimate. Eurostat publishes data on the revisions of the euro

area (EA-12, including the 12 first members of the euro area) on its website (14

). At the time of preparing this

article, data were available from 2003Q1 to 2013Q4 for the flash (t+45), second (t+65) and third (t+100)

estimates. Table 1 below shows the average and absolute average revision made to the t+45 estimates

compared to the t+65 and t+100 estimates.

(11) Eurostat published the European aggregates at t+100 for quarters up to 2014Q3. As t+100 estimates have not been published since 2014Q3, in

Section 5 the t+30 test estimates are compared with t+45, t+65 and with the t+65 publication concerning the following quarter – i.e. at t+3 months + 65 days after the reference quarter under review. In Sub-section 4.3, when discussing what t+30 revisions could be, the t+45 flash GDP growth rates since 2003Q1 are still compared with Eurostat t+65 and t+100 estimates which is enabled by the longer back history of t+45 estimates. Correspondingly, the US t+30 estimates average revision are compared with t+60 and t+90 US estimates.

(12) For instance, (Zwijnenburg, 2015) provides an update on OECD country revision performances.

(13) In order to allow publication at t+30 days in 2016, national GDP flash data will need to be provided before 16.00h one day before.

(14) http://ec.europa.eu/eurostat/web/national-accounts/data/other

Table 1: Average revisions to quarter-on-quarter GDP t+45 growth of the euro area (EA-12)

at 65 and 100 days, in 2003Q1 – 2013Q4

(percentage points of GDP growth)

Source: Eurostat calculations

Over this 11-year period, the revision performance of the GDP t+45 flash estimate for the EA-12 was very

good. The revision performance of the t+45 estimates for the EU was similar to that for the EA-12, shown in

table 1.

To put these data into context, and also as a starting point for fixing the criteria to be met by the GDP t+30

flash estimate, it is worth considering the revisions made to the US GDP flash estimate, which is published at

t+30. These were as shown in table 2, over the period from 2003Q1 to 2014Q3:

Table 2: Average revisions to quarter-on-quarter GDP t+30 growth of the United States at 60

and 90 days, in 2003Q1 – 2014Q3

(percentage points of GDP growth)

Source: Eurostat calculations. NB: US publishes annualised quarter-on-quarter growth rates. For comparison here the annualised growth rates have been transformed back to plain quarter-on-quarter growth rates which are comparable with the ones given for the euro area and the EU.

As can be seen from the tables 1 and 2, the US appears to revise its estimate more than has been necessary for

the EA-12 estimate, with the absolute revision in particular being significantly larger. There is of course a

variety of reasons why this might be the case, including the fact that the US flash estimate is produced 15 days

earlier. The revisions made to the US estimates will be taken into consideration when setting the acceptance

criteria for accuracy for the GDP t+30 flash estimates for the euro area and the EU.

As a minimum, the GDP t+30 flash estimate needs to be an unbiased estimate of the GDP t+45 figure. In other

words, the frequency of upwards and downwards revisions should be broadly equal, and the average revision

should be not statistically significantly different from 0. Performing a statistical test on such a short run of

observations would, unfortunately, be difficult. Using a student’s t-test on a sample of this size would result in

a high probability of a ‘type II error’, leading to the null hypothesis being accepted on false grounds, i.e.

concluding that there is no bias when there is. See Annex B for more details.

In addition, as mentioned in Sub-section 4.2, it is necessary to set deadlines by which Member States are

required to submit their data. This will ensure that Eurostat always receives the data with enough time to

produce the GDP estimates for the euro area and the EU by the t+30 deadline. As the first publication was

scheduled for April 2016, it was considered sufficient to test whether the four quarters of 2015 are transmitted

to Eurostat in time (i.e. at t+29 days).

4.4 The acceptance criteria

The previous sections have looked at the meaning of the quality of statistics and the factors that need to be

taken into consideration when setting the acceptance criteria. Given the options available as criteria and the

limitations of the data, the following three main acceptance criteria were adopted.

Average revisionAverage absolute

revision

t+45 to t+65 0.00 0.02

t+45 to t+100 0.00 0.03

Average revisionAverage absolute

revision

t+30 to t+60 0.02 0.13

t+30 to t+90 0.02 0.16

1. Unbiased GDP t+30 flash estimate

The GDP t+30 flash estimate should be an unbiased estimate of the t+45 estimate of GDP growth, with an

average revision between -0.05 and +0.05 percentage points, and no more than 66.7% of revisions in the same

direction.

This criterion has been set to test for bias. The ideal way of testing this bias would be to perform a statistical

test. As the sample is too small to perform this type of test (see Annex B), the recommendation is therefore to

use the boundaries -0.05 and +0.05. In order to avoid a scenario where a small number of large revisions in one

direction (plus or minus) offset a large number of smaller revisions in the other direction, the criterion also

includes a test on the percentage of revisions in each direction (tested at publication level, i.e. to one decimal

place).

This criterion should be tested on all the available test data (from the first flash estimate in 2012Q1 onwards)

and kept under review once the estimates start to be published.

2. Limited average absolute revision

The average absolute revision made to the t+30 estimate of GDP growth should be: i) less than or equal to 0.10

percentage points when the t+45 estimate is published; and ii) less than or equal to 0.13 percentage points

when the t+65 estimate is published.

This criterion has been set to ensure that the level of revisions made to the GDP t+30 flash estimate is

acceptable. In theory, the first part of criterion 1 (that the average revision must be between -0.05 and +0.05

percentage points) could be met if there were large offsetting revisions in both directions, which would be

undesirable. Criterion 2 will guard against this. When setting these boundaries, particular consideration was

given to the revisions made to the US early estimates of GDP over the period 2012Q1 to 2014Q3. An

overview of the revisions to early estimates of US GDP growth is attached as Annex C (15

). Although it could

be argued that the revisions made to GDP estimates for the euro area and the EU could be expected to be

smaller than those for the US statistics, it should also be kept in mind that the GDP t+30 flash estimates for the

euro area and the EU are developing statistics. As mentioned in Sub-section 4.3, a substantial number of

Member States produced the data for the quarters between 2012Q1 and 2013Q4 on a purely theoretical basis,

without having the opportunity to make use of expert judgement. It can be assumed that expert judgement

would improve these early estimates, and therefore that the revisions needed should decrease over time. On the

basis of these considerations, the limits that have been set are quite similar to the revisions made to US

statistics.

This criterion should be tested on data from all test quarters.

3. Sufficient coverage

For the final two quarters of 2015, Eurostat needs to receive estimates from Member States whose combined

GDP in the previous year accounted for 70% of total GDP for the euro area and the EU respectively by the

t+29 deadline.

This criterion will ensure sufficient coverage. It has also been set to safeguard against the publication of a GDP

t+30 flash estimate before it has been proven that it will be possible to deliver the estimate consistently by this

date. This criterion will reduce the likelihood of insufficient data being available to produce good quality GDP

t+30 flash estimates for the euro area and the EU once data releases begin. In addition to meeting this criterion,

there should also be no known reasons why the criteria would not be met for every quarter in 2016. This

should be ensured by obtaining commitment from the representatives of the Member States involved.

The acceptance criteria described above have been applied to the GDP t+30 test estimates for the euro area and

the EU. The next section assesses the GDP t+30 test estimates against the quality acceptance criteria.

(15) Annex C provides data on revisions to US estimates over a slightly longer period: 2012Q1-2015Q2.

5. Results and assessment of the GDP t+30 test

estimates

5.1 Introduction

The previous sections discussed the method used to prepare the GDP t+30 test estimates for the euro area and

the EU and explained the quality acceptance criteria to be used for assessing these test estimates. This section

will present the results for the 16 test quarters and compare these results with the GDP estimates released at

t+45 days, t+65 days and at t+3 months + 65 days (the t+45 flash estimate, the ‘regular’ t+65 estimate and the

estimate for the current quarter when publishing the ‘regular’ t+65 estimate for the next quarter). It analyses

the revisions made to the GDP t+30 estimates at each of these dates (i.e. the difference between the GDP t+30

estimate and each of the above-mentioned later estimates) and assesses the GDP t+30 test estimates against the

quality acceptance criteria.

Sub-section 5.2 briefly presents the test estimates and Sub-section 5.3 assesses these results against the quality

acceptance criteria, as set out in Section 4.

5.2 Results of the GDP t+30 test estimates

To assess the feasibility of estimating the quarter-on-quarter and year-on-year GDP growth in the euro area

and the EU at 30 days after the quarter-end, Eurostat, in cooperation with the participating Member States,

compiled 16 GDP t+30 test flash estimates. Eight of the test estimates were produced retrospectively for past

quarters from 2012 and 2013 and eight estimates were compiled in real-time during 2014 and 2015.

For the retrospectively produced quarters, Member States were asked to provide estimates calculated using

only primary source data that would have been available 29 days after the end of the reference quarter. Real-

time t+30 estimates could be used for the UK, Belgium, Spain and Lithuania as these countries were already

publishing GDP t+30 estimates at the time.

For the real-time estimated quarters, the participating Member States were asked to provide their estimates to

Eurostat 29 days after the end of the reference quarter. The data provided by the various Member States

included published estimates (as mentioned above) for the UK, Belgium, Spain and Lithuania, and, from

2014Q3 onwards, also for Austria and Latvia. Using the estimates provided by all participating Member

States, Eurostat then compiled the real-time GDP t+30 flash estimates for the euro area and the EU.

Table 3 below compares the test t+30 and the t+45 flash estimates for quarter-on-quarter GDP growth in the

euro area. Table 4 shows the corresponding data for the EU. (16

)

(16) All the t+30 test estimates in tables 3 and 4 were produced by using only the Member States' test estimates. Here no top-up e.g. with the ESI was

used.

Table 3: Euro area, test t+30 and t+45 flash estimates of GDP growth

(quarter-on-quarter GDP growth rates, %; revisions to growth rates, percentage points)


Table 4: EU, test t+30 and t+45 flash estimates of GDP growth



5.3 Assessment of GDP t+30 test estimates

Table 3 shows that the revisions to the published data (growth rate given to one decimal place) for the GDP

t+30 estimates for the euro area would have been 0.0 six times (38%), +0.1 five times (31%), -0.1 four times

(25%) and -0.2 on one occasion (6%), meaning there would have been five downward revisions (31%), and

also five upward revisions (31%). Table 4 shows that revisions to the published data for the EU would have

been 0.0 nine times (56%), -0.1 four times (25 %) and +0.1 three times (19%), meaning there would have been

four downward revisions (25%) and three upward revisions (19%). The average revisions, when comparing

figures at t+30 and t+45 given to two decimal places, are 0.00 for the euro area and -0.01 for the EU. Both the

number of revisions in each direction and the average revision to be made between the t+30 and the t+45

t+30 test t+45Revision

t+45 - t+30t+30 test t+45

Revision

t+45 - t+30% of GDP

Number of

Member

States

2012Q1 EA-17 -0.06 0.02 0.08 -0.1 0.0 0.1 70 7

2012Q2 EA-17 -0.07 -0.18 -0.11 -0.1 -0.2 -0.1 70 7

2012Q3 EA-17 0.07 -0.05 -0.13 0.1 -0.1 -0.2 91 8

2012Q4 EA-17 -0.51 -0.59 -0.08 -0.5 -0.6 -0.1 91 8

2013Q1 EA-17 -0.21 -0.22 -0.01 -0.2 -0.2 0.0 70 7

2013Q2 EA-17 0.31 0.27 -0.04 0.3 0.3 0.0 91 8

2013Q3 EA-17 0.11 0.09 -0.02 0.1 0.1 0.0 91 8

2013Q4 EA-17 0.26 0.28 0.02 0.3 0.3 0.0 91 8

2014Q1 EA-18 0.28 0.19 -0.10 0.3 0.2 -0.1 70 8

2014Q2 EA-18 0.07 0.05 -0.03 0.1 0.0 -0.1 63 8

2014Q3 EA-18 0.13 0.16 0.03 0.1 0.2 0.1 88 9

2014Q4 EA-18 0.22 0.34 0.12 0.2 0.3 0.1 94 10

2015Q1 EA-19 0.29 0.40 0.11 0.3 0.4 0.1 73 10

2015Q2 EA-19 0.27 0.31 0.04 0.3 0.3 0.0 94 11

2015Q3 EA-19 0.26 0.30 0.04 0.3 0.3 0.0 94 11

2015Q4 EA-19 0.24 0.27 0.03 0.2 0.3 0.1 94 11

QuarterComposition

euro area

Compilation level Publication level Coverage

t+30 test t+45Revision

t+45 - t+30t+30 test t+45

Revision

t+45 - t+30% of GDP

Number of

Member States

2012Q1 EU-27 -0.03 -0.05 -0.01 0.0 0.0 0.0 70 12

2012Q2 EU-27 -0.10 -0.16 -0.06 -0.1 -0.2 -0.1 73 13

2012Q3 EU-27 0.25 0.13 -0.12 0.2 0.1 -0.1 86 13

2012Q4 EU-27 -0.48 -0.51 -0.04 -0.5 -0.5 0.0 86 13

2013Q1 EU-27 -0.08 -0.11 -0.03 -0.1 -0.1 0.0 70 12

2013Q2 EU-27 0.35 0.32 -0.03 0.3 0.3 0.0 89 14

2013Q3 EU-28 0.26 0.24 -0.02 0.3 0.2 -0.1 86 13

2013Q4 EU-28 0.37 0.39 0.03 0.4 0.4 0.0 86 13

2014Q1 EU-28 0.42 0.32 -0.09 0.4 0.3 -0.1 71 14

2014Q2 EU-28 0.22 0.18 -0.04 0.2 0.2 0.0 65 13

2014Q3 EU-28 0.27 0.30 0.03 0.3 0.3 0.0 85 15

2014Q4 EU-28 0.30 0.38 0.08 0.3 0.4 0.1 90 17

2015Q1 EU-28 0.34 0.42 0.08 0.3 0.4 0.1 75 16

2015Q2 EU-28 0.38 0.41 0.03 0.4 0.4 0.0 92 17

2015Q3 EU-28 0.31 0.37 0.06 0.3 0.4 0.1 90 16

2015Q4 EU-28 0.31 0.35 0.03 0.3 0.3 0.0 91 17

QuarterComposition

EU

Compilation level Publication level Coverage

estimate are therefore within the limits allowed by the first quality criterion as specified in Sub-section 4.4 (an

unbiased GDP t+30 flash estimate for the euro area and the EU).

As can be seen from Tables 3 and 4 above, the coverage of the GDP t+30 estimates varied between 63% and

94% of total GDP for the euro area, and between 65% and 92% of total GDP for the EU. During the final two

quarters of 2015, the coverage has been at an average of 94% of GDP for the euro area and 91% for the EU.

The test estimates therefore clearly meet the coverage criterion as specified in Sub-section 4.4 (coverage

should be more than 70% of total GDP for the euro area and the EU respectively).

The performance of the t+30 quarter-on-quarter GDP growth estimates is further analysed in Tables 5 (for the

euro area) and 6 (for the EU). A similar analysis for the t+30 estimates of year-on-year GDP growth is given in

Tables 7 (for the euro area) and 8 (for the EU).

Table 5: GDP t+30 test estimates and revisions for the euro area



t+30 t+45 t+65t+3m+65

dt+45 t+65 t+3m+65d

2012Q1 -0.06 0.02 -0.01 -0.02 0.08 0.05 0.04

2012Q2 -0.07 -0.18 -0.17 -0.17 -0.11 -0.09 -0.10

2012Q3 0.07 -0.05 -0.05 -0.07 -0.13 -0.12 -0.14

2012Q4 -0.51 -0.59 -0.59 -0.59 -0.08 -0.09 -0.08

2013Q1 -0.21 -0.22 -0.21 -0.16 -0.01 0.00 0.05

2013Q2 0.31 0.27 0.29 0.30 -0.04 -0.01 -0.01

2013Q3 0.11 0.09 0.08 0.15 -0.02 -0.03 0.04

2013Q4 0.26 0.28 0.28 0.26 0.02 0.02 0.00

2014Q1 0.28 0.19 0.18 0.22 -0.10 -0.10 -0.06

2014Q2 0.07 0.05 0.03 0.07 -0.03 -0.04 0.00

2014Q3 0.13 0.16 0.16 0.18 0.03 0.03 0.06

2014Q4 0.22 0.34 0.33 0.36 0.12 0.11 0.14

2015Q1 0.29 0.40 0.37 0.52 0.11 0.08 0.23

2015Q2 0.27 0.31 0.36 0.39 0.04 0.09 0.12

2015Q3 0.26 0.30 0.29 : 0.04 0.03 :

2015Q4 0.24 0.27 : : 0.03 :

0.00 0.00 0.02

0.06 0.06 0.08

0.07 0.07 0.10

Average revision

Average absolute revision

Root of the mean squared errors (RMSQE)

GDP growth rates Revisions to t+30 estimate at

Table 6: GDP t+30 test estimates and revisions for the EU



Table 7: GDP t+30 test estimates and revisions for the euro area

(year-on-year GDP growth rates, %; and revisions to growth rates, percentage points)


t+30 t+45 t+65 t+3m+65d t+45 t+65 t+3m+65d

2012Q1 -0.03 -0.05 -0.02 -0.02 -0.01 0.01 0.01

2012Q2 -0.10 -0.16 -0.14 -0.15 -0.06 -0.04 -0.05

2012Q3 0.25 0.13 0.12 0.11 -0.12 -0.13 -0.14

2012Q4 -0.48 -0.51 -0.49 -0.50 -0.04 -0.01 -0.02

2013Q1 -0.08 -0.11 -0.06 -0.05 -0.03 0.02 0.03

2013Q2 0.35 0.32 0.36 0.36 -0.03 0.01 0.01

2013Q3 0.26 0.24 0.23 0.31 -0.02 -0.03 0.05

2013Q4 0.37 0.39 0.42 0.39 0.03 0.05 0.03

2014Q1 0.42 0.32 0.30 0.33 -0.09 -0.11 -0.08

2014Q2 0.22 0.18 0.16 0.23 -0.04 -0.06 0.01

2014Q3 0.27 0.30 0.30 0.32 0.03 0.02 0.05

2014Q4 0.30 0.38 0.41 0.43 0.08 0.11 0.14

2015Q1 0.34 0.42 0.44 0.54 0.08 0.10 0.20

2015Q2 0.38 0.41 0.45 0.46 0.03 0.06 0.08

2015Q3 0.31 0.37 0.37 : 0.06 0.06 :

2015Q4 0.31 0.35 : : 0.03 : :

-0.01 0.00 0.02

0.05 0.05 0.06

0.06 0.07 0.08

Average revision




t+30 t+45 t+65 t+3m+65d t+45 t+65 t+3m+65d

2012Q1 -0.07 0.01 -0.05 -0.05 0.08 0.02 0.02

2012Q2 -0.28 -0.39 -0.46 -0.46 -0.11 -0.18 -0.19

2012Q3 -0.46 -0.58 -0.61 -0.61 -0.12 -0.15 -0.15

2012Q4 -0.78 -0.86 -0.89 -0.96 -0.08 -0.11 -0.18

2013Q1 -1.04 -1.05 -1.11 -1.02 -0.01 -0.07 0.01

2013Q2 -0.66 -0.70 -0.45 -0.57 -0.04 0.21 0.09

2013Q3 -0.35 -0.37 -0.36 -0.29 -0.02 0.00 0.07

2013Q4 0.48 0.50 0.52 0.50 0.02 0.04 0.02

2014Q1 0.97 0.88 0.90 0.95 -0.09 -0.08 -0.02

2014Q2 0.68 0.66 0.67 0.80 -0.02 0.00 0.12

2014Q3 0.75 0.78 0.79 0.80 0.03 0.04 0.05

2014Q4 0.76 0.88 0.86 0.87 0.12 0.10 0.11

2015Q1 0.88 0.99 1.01 1.24 0.11 0.14 0.37

2015Q2 1.18 1.22 1.53 1.59 0.04 0.35 0.41

2015Q3 1.53 1.57 1.59 0.04 0.06 :

2015Q4 1.47 1.49 : : 0.03 : :

0.00 0.02 0.05

0.06 0.10 0.13

0.07 0.14 0.18




Average revision

Table 8: GDP t+30 test estimates and revisions for the EU

(year-on-year GDP growth rates, %; revisions to growth rates, percentage points)


The four tables above compare the GDP growth rate at t+30 days with the estimates published at t+45 days

(first estimate), at t+65 days (second estimate), and after three months plus 65 days. The last growth vintage

allows for assessing how the GDP t+30 estimate for the reference quarter has changed by the time of

publication of the ‘regular’ 65 days’ estimate for the next quarter. The revisions are calculated as the later

estimate minus the t+30 estimate, e.g. the estimate produced at t+45 minus the estimate at t+30. The average

revisions, average absolute revisions and the root of the mean squared errors (RMSQE) are given in each table.

As can be seen in Tables 5 and 6, the average absolute revisions made to the t+30 estimate of the quarter-on-

quarter GDP growth rates at t+45 and t+65 were 0.06 percentage points for the euro area and 0.05 percentage

points for the EU (each at both points in time). The second quality criterion given in Sub-section 4.4 requires

that the difference between the t+45 and t+30 estimates be less than or equal to 0.10 percentage points and the

difference between the t+65 and t+30 estimates be less than or equal to 0.13 percentage points. The GDP t+30

test estimates for the euro area and the EU therefore also fulfil the second quality criterion.

It should be noted that the average absolute revisions made to the t+30 estimates of quarter-on-quarter GDP

growth for the euro area only slightly increased when the ‘regular’ 65 days’ estimate for the subsequent

quarter was available (the absolute average revision at this point being 0.08 percentage points, where it was

0.06 percentage points at 45 and 65 days after the end of the reference quarter). The average absolute revision

for the EU was 0.06 percentage points on releasing the 65 days’ estimate for the following quarter, which was

only 0.01 percentage points higher than it had been at t+45 and t+65.

As can be seen in Tables 7 and 8, the average absolute revisions to the GDP t+30 year-on-year growth are only

slightly larger, for both the euro area and the EU. The same pattern has been seen for the t+45 flash.

t+30 t+45 t+65 t+3m+65d t+45 t+65 t+3m+65d

2012Q1 0.15 0.14 0.11 0.10 -0.01 -0.04 -0.05

2012Q2 -0.18 -0.24 -0.29 -0.32 -0.06 -0.11 -0.13

2012Q3 -0.23 -0.35 -0.41 -0.36 -0.13 -0.18 -0.14

2012Q4 -0.58 -0.61 -0.59 -0.66 -0.03 -0.01 -0.08

2013Q1 -0.64 -0.67 -0.68 -0.65 -0.03 -0.04 -0.01

2013Q2 -0.21 -0.24 -0.03 -0.14 -0.03 0.17 0.06

2013Q3 0.08 0.06 0.08 0.21 -0.02 0.00 0.14

2013Q4 0.97 0.99 1.06 1.05 0.02 0.09 0.08

2014Q1 1.51 1.41 1.40 1.43 -0.10 -0.11 -0.08

2014Q2 1.25 1.21 1.20 1.34 -0.04 -0.05 0.10

2014Q3 1.26 1.29 1.30 1.25 0.03 0.04 -0.02

2014Q4 1.23 1.32 1.30 1.30 0.08 0.07 0.07

2015Q1 1.28 1.36 1.45 1.68 0.08 0.17 0.39

2015Q2 1.58 1.61 1.87 1.69 0.03 0.29 0.11

2015Q3 1.80 1.86 1.89 : 0.06 0.09 :

2015Q4 1.72 1.76 : 0.03 : :

-0.01 0.03 0.03

0.05 0.10 0.10

0.06 0.12 0.14

Average revision




Overall, the GDP t+30 test estimates for the euro area and the EU met all the predefined quality acceptance

criteria.

The revisions to the first officially published GDP t+30 estimates for 2016Q1 continued to be small and to

meet well all the quality acceptance criteria.

6. Conclusions

The research question for this article was: Estimating reliably European GDP at 30 days after the quarter-end

– is that feasible? The core of this article concerns the description of the estimation method and the assessment

of the estimates for the test quarters against the predefined acceptance criteria.

The method developed for producing preliminary flash estimates of quarterly GDP for the euro area and the

EU 30 days after the end of the quarter is in many respects similar to the method currently used for the euro

area and EU GDP t+45 flash estimates. The main differences are that the t+30 estimate has a slightly limited

country coverage and that greater use is made of preliminary country estimates (data for the third month often

having to be estimated or partially estimated by the Member State at this earlier date). The methodology for

producing GDP t+30 (test) flash estimates for the euro area and the EU is characterised by the following

features:

The flash estimates for the EU and the euro area are produced using the indirect approach, i.e. Member

States flash estimates and/or indicators at t+29 (17

) are used as the main data source, rather than

indicators at a European level.

All available information is used as far as possible:

All GDP t+30 flash estimates that are available from the Member States for the reference quarter

will be used. This is the case irrespective of whether the country’s GDP t+30 estimate has been

published at t+30 days or whether it is unpublished and is provided confidentially to Eurostat

exclusively for the purpose of producing the GDP t+30 flash estimate of the European aggregates.

Other relevant indicators may be used for a (major) Member State if its GDP t+30 estimate is not

available. These alternative indicators are mainly short-term economic statistics, such as the

industrial production index, deflated real trade and the turnover of services, for which two

months’ data are available and the third month can be nowcast. The economic sentiment indicator

(ESI) may also be used. Furthermore, the forecasts issued by forecasters may be considered as

secondary information in case a decision is needed on a growth estimate for a missing data

(major) country.

The decision to start publishing the GDP t+30 flash estimates for the euro area and the EU was based

on the results of a testing phase carried out over the period 2012-2015. The GDP t+30 flash estimates

for the euro area and the EU for the quarters from 2012Q1to 2013Q4 were calculated retrospectively,

and the Member States involved were asked to use only the data that would have been available within

30 days of the end of the reference quarter when supplying their national estimates. The estimates for

the quarters from 2014Q1 to 2015Q4 were calculated in real time.

Flash estimates are available earlier than traditional estimates. There is a trade-off between timeliness

and accuracy. Based on the 16 test estimates, the expected revision of the GDP t+30 growth rates at

t+45 would be ± 0.1 percentage points for the euro area at publication level (i.e. considering the

published figures at the two points in time, which are given to one decimal place). For the EU, the

revision was 0.0 percentage points in nine of the 16 quarters and ± 0.1 percentage points in the other

(17) Member States are requested to transmit their national estimates to Eurostat one working day before publication of euro area and EU GDP t+30

estimates.

seven. If there were to be a sudden dramatic change in economic trends, as was seen in 2008Q2 when

the financial crisis broke, larger revisions than those mentioned above might be expected.

The expected revisions have been tested against quality criteria set a priori. Over the 16 test quarters,

the average revision made to the GDP t+30 flash estimates when publishing the t+45 estimates was

0.00 percentage points for the euro area and -0.01 percentage points for the EU (the quality criterion

requires these values to be between -0.05 and 0.05 percentage points). The average absolute revision

made to the GDP t+30 flash estimates when publishing the t+45 estimates was 0.06 percentage points

for the euro area and 0.05 percentage points for the European Union (the quality criterion requires these

values to be less than 0.10 percentage points). Comparing the GDP t+30 estimates with those produced

at t+65, the average absolute revision would also have been 0.06 percentage points in the euro area and

0.05 percentage points in the European Union. The quality criterion requires these values to be less than

or equal to 0.13 percentage points, a level set on the basis of the revision typically made between US

t+30 and t+60 GDP estimates. The test results therefore fulfil the a priori determined quality criteria.

The good results of the GDP t+30 project (with test estimates showing that only limited revisions have been

necessary, and coverage of all test estimates already at a higher level than achieved for the GDP t+45 estimates

when they were first released) indicated that the release of GDP estimates for the euro area and the EU can be

brought forward to 30 days after the end of the reference period. Therefore, Eurostat decided in December

2015 to start releasing the GDP estimates for the euro area and the EU 30 days after the quarter-end, beginning

with the first quarter of 2016. The revisions to the first officially published GDP t+30 estimates for 2016Q1

continued to be small and to meet well all the quality acceptance criteria.

A large number of Member States contribute to the GDP t+30 estimates for the euro area and the EU by

providing their national estimates. The launching of the preliminary GDP flash estimates around 30 days is

seen as an achievement of the whole European Statistical System (ESS).

Based on all above, this paper can be concluded: Estimating reliably (enough) the European GDP at 30 days

after the quarter-end has proven to be feasible.

Acknowledgements

The authors would like to thank all those who have contributed to the work of the GDP at t+30 project and to

the preparation of this article. In the early part of the development work substantial support was received from

Ingo Kuhnert (DG ECFIN). Particular thanks also go to Robert Doody (UK), who coordinated the task force

work for Section 4 and Appendix B, and to Ben Gardiner, Wojtek Szewczyk and Adam Brown (all three from

Cambridge Econometrics) on their work with the possible top-up of the sample to population estimator by the

economic sentiment indicator.

Last but not least the authors would like to thank all members of the task force that contributed to the GDP at

t+30 project: Milen Kolev (Bulgaria), Kornel Mahlstein/Stefan Leist (Switzerland), Michal Siroky/Karel

Safr/Tereza Koštáková (Czech Republic), Erich Oltmanns/Christian Mueller/Tanja Mucha (Germany), Samu

Hakala (Finland), Hélène Soual/Alexis Louvel/Thomas Laurent/Philippe Gallot (France), Anikó Száraz

(Hungary), Filippo Moauro (Italy), Kristina Kiriliauskaite (Lithuania), Alina Sadovska/Andris Kalnins/Gita

Kinkevska (Latvia), Nico van Stokrom (The Netherlands), Piotr Markuszewski/Pawel Markocki/Joanna

Kozicka/Irmina Cerling (Poland), Carla Grosa (Portugal), Alina Predescu (Romania), Anže Podnar (Slovenia),

Robert Doody (United Kingdom), Stanimira Kosekova (ECB), Wojtek Szewczyk/Shalini Mittal/Adam

Brown/Ben Gardiner (Cambridge Econometrics), and Silke Stapel-Weber/Ani Todorova/Arto Kokkinen/Hans

Wouters (Eurostat). The Member State representatives contributed to the work of the task force by providing

information on their data sources, by developing methods for producing early estimates and/or by providing

quarterly national GDP estimates to be used for producing the test estimates for the euro area and the EU.

Without their contributions, the project could not have been concluded successfully.

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Annexes

Annex A: Aggregation of the country growth rates

This Annex explains how the Member States’ chain-linked volume growth rates are aggregated to compile the

EU and euro-area growth rates.

The following notation will be used (reflecting the notation used in the Handbook on quarterly national

accounts (Eurostat 2013, pp. 190-191)):

The aggregate variable X at quarter c of year y in current prices is denoted by ,c y

CPX , in prices of the

previous year by ,c y

PPYX , and for chain-linked volumes by ,c y

CVX .

The implicit price deflator of the chain-linked volume indices is denoted by

,,

,

c yc y CP

X c y

CV

XP

X .

Measures indexed by a year only denote annual data, e.g. y

CPX (the current price value of the

aggregate X in year y) and

yy CP

X y

CV

XP

X is the implicit price deflator of X in the same year.

Chain-linked volume indices have to be referenced to a value in a particular period, usually at 100 or

the current price value in the reference year, thus 0 100CVX or

0 0

CV CPX X .

The annual chain-linked volume growth between y and y-1 can be calculated as 1 1

y y

CV PPY

y y

CV CP

X X

X X (where

the latter is the Laspeyres type volume index 1

yy PPYQ y

CP

XL

X ).

An annual chain Laspeyres volume index referenced to the current price value in year 0 can therefore be

expressed as

0

11

myy PPY

CV CPmm CP

XX X

X

.

In the case of annual overlap quarterly chain-linking method (used by Eurostat and the common practice in

most EU countries) the quarterly previous year price figures refer to average prices of the previous year. This

means that the quotient of a variable given in the previous year’s prices and the corresponding chain-linked

volume estimate is equal to the annual implicit price deflator of the previous year

1,1

, 1

yc y yyCPPPY PPY

Xc y y y

CV CV CV

XX XP

X X X

.

The following section first explains the background to the aggregation of annual country (or component)

growth rates to give the annual growth rate of the aggregate. It then discusses the use of the annual current

price weights for the year y-1 in aggregating Member States’ chained quarter-on-quarter GDP growth rates to

produce aggregates for the euro area and the EU.

Annual case

The relative growth rate of the chain-linked volumes (CV) for an individual country i is calculated by

A.1

1 1

, , , ,

1 1

, ,

y y y y

CV i CV i PPY i CP i

y y

CV i CP i

x x x x

x x

. Multiplying both sides of the equation by

1

,

y

CP ix gives

A.2 ,1 1

, , ,1

,

1

y

CV iy y y

CP i PPY i CP iy

CV i

xx x x

x

. This equation shows that, when multiplying the annual

chain-linked volume relative growth by the current price figure at y-1, the result is the absolute volume growth

between year y in the previous year’s prices and year y-1 in current prices. Dividing both sides of formula A.2

above for country i by the same formula expressed for the European aggregate gives

A.3

,1

, 1 1, , ,

1

1

1

1

1

y

CV iy

CP i y y yCV i PPY i CP i

y yyy PPY CPCV

CP y

CV

xx

x x x

X XXX

X

.

Now, multiplying both sides of the above by the chain-linked volume growth rate of the aggregate, i.e. by

11

y

CV

y

CV

X

X

, gives:

A.4

1 1

, , , ,

1 1 1 1

,

1 1

y y y y yCP i CV i PPY i CP i CV

y y y y y

CP CV i PPY CP CV

x x x x X

X x X X X

.

The right-hand side of equation A.4 shows that the chain-linked relative volume growth rate of the aggregate is

multiplied by a term in which the absolute volume growth of component ix is expressed as a proportion of the

absolute volume growth of the aggregate X . The result is thus the contribution made by the volume growth of

componentix to the relative volume growth of the aggregate X .

The left-hand side of the equation A.4 shows that the contribution made by the same component ix to the

relative volume growth of the aggregate X can also be calculated by multiplying the relative growth rate of the

componentix by the current price level of the component

ix over the current price level of the aggregate X in

year y-1.

Quarterly case

The Handbook on quarterly national accounts (Eurostat 2013, pp. 200-204) discusses different methods for

calculating the growth contributions of the components to the quarter-on-quarter chain-linked volume growth

of the aggregate variable, such as GDP. The method discussed above, applied to the quarter-on-quarter growth

rate of the component ix of the aggregate X , is called the weighted growth rates (WGR) method. In our

example, using annual current prices as the weights, the formula is:

A.5

1 , 1, 1 ,

, , , , ,,

1 1, 1 1,

, ,

. ( , ) 1

y c y c y y c y

CP i CV i CV i CP i CV iA c y

i y c y y c y

CP CV i CP CV i

x x x x xContribWGR x X

X x X x

In the case of European aggregates, when the Laspeyres chained- volume index is used, together with the

annual overlap quarterly chain-linking methodology, the current price figure for year y-1 forms the moving

base period for the volume calculation. A natural choice is therefore to use the weighted growth rates method

described above with annual weights. It is worth noting that, as mentioned in the Handbook on quarterly

national accounts (Eurostat 2013, p. 204), the attractions of the WGR method are that it is simple to use and

easy to understand and it is independent of the quarterly linking method. The Handbook on quarterly national

accounts (Eurostat 2013, pp. 203-204) suggests it as one method for calculating the contribution made by the

component ix to the quarter-on-quarter volume growth of the aggregate X . This method is used in calculating

the t+30 and t+45 flash estimates of the quarterly GDP for the euro area and the EU. The quarter-on-quarter

growth estimates provided by the Member States are aggregated using the equation A.5 above.

It is worth noting, though, that the contributions calculated using this method are not exactly additive in the

quarterly case. This is most visible in the case of the quarter-on-quarter growth rate between Q1 and Q4, as the

former has year y-1 as a base year and the latter year y-2. The Handbook on quarterly national accounts

(Eurostat 2013, pp. 200-204) discusses another additive volume data method, which includes a correction for

the first quarter, the effect of which is that the quarterly contributions will add up exactly to the same

contribution of the component in the annual data. Finally, the Handbook discusses how a correction factor can

be introduced into the WGR method (using annual or quarterly weights), in order to obtain results for the

contributions of the components that are exactly additive:

A.6

1,

,1,

, ,

1

,1

. ( , ) . ( , )

c y

CV ic y

A c y c yCVi iy

CV iy

CV

x

XContribWGR x X Contrib AVD x X

x

X

.

In practice, when aggregating the country growth rates to give the euro-area and EU totals, the size of the

correction that would need to be made to the aggregate relative growth rate is quite small, e.g. between

2010Q1 and 2015Q2, the average absolute value of the correction was 0.0004%. The proportions of the

Member States’ GDPs in the aggregate GDP are rather stable, both between quarters and between years.

Annex B: Sample size for testing revisions for bias

Introduction

This Annex discusses the effect on the results of a student’s t-test in the case of having a small number of

observations. It examines the method used by the UK to test whether the revisions to economic indicators

would be biased. Finally, the Annex considers whether the limited number of observations available from the

testing phase of the GDP t+30 flash estimate rules out the use of a statistical test in assessing the possible bias

in revisions.

Terminology

Type 1 error: rejecting the null hypothesis when it is true (i.e. saying there is bias when there is not).

Significance level: the probability of a type 1 error (i.e. the probability of saying there is bias when

there is not).

Type 2 error: accepting the null hypothesis when the alternative hypothesis is true (i.e. saying there is

no bias when there is).

Power: 1 minus the probability of a type 2 error (i.e. the probability of correctly identifying bias).

Method

The current method for testing for bias in the revisions to early estimates of economic indicators in the UK is

to use t-tests to test for bias. This method was recommended in the paper "An examination of the way CSO

[the Chief Scientist Office] tests for bias in the initial estimates of major economic indicators; some suggested

improvements". (Dr C. Chatfield, CSO Research Project, University of Bath).

For the annual series, the t-test assumes that revisions are independent.

The test statistic is calculated as

x

xt

s , where:

x is the average revision

22

x

ss

n , where:

2s is the population variance in the revisions (estimated using the sample)

n is the sample size.

The test statistic is compared to a t-distribution with n degrees of freedom. The significance level used is 0.05,

meaning that the probability of a type 1 error is 0.05 or 5%.

For the quarterly series, an adjusted t-test is used, which assumes that revisions follow an AR(1) process

(meaning that the revision at one time point depends on the revision made at the previous time point).

The test statistic is calculated as *2

x

xt

s , where:

x is the average revision.

2*2 (1 )

(1 )x

ss

n

, where:

2s is the population variance in the revisions (estimated using the sample)

n is the sample size

is an estimate of the correlation between revisions at time t and time t-1.

The test statistic is compared to a t-distribution with 2

2

(1 )

(1 )n

degrees of freedom. The significance level used

is 0.05, meaning that the probability of a type 1 error is 0.05 or 5%.

Impact of reducing the sample size on type 1 errors

If the sample size were to be reduced, then the critical value used to compare the test statistic should be

changed to reflect the change in the degrees of freedom. If the significance level remained unchanged, then the

probability of a type 1 error would also remain unchanged.

The critical value for a two-sided t-test with a significance level of 0.05 and a sample size of 14 is 2.145.

Impact of reducing the sample size on the power of the test

The problem created by a smaller sample size is that it reduces the power of the test. The power of the test

depends on the sample size, the effect size and the significance level.

The effect size puts into context how large the average revision is in relation to the spread of the revisions. It is

calculated as the mean of the revisions divided by the standard deviation of the revisions (i.e. the t-test statistic

divided by the square root of the number of observations).

xd

s , where:

x is the average revision

2s is the population variance in the revisions (estimated using the sample).

Figure 1 below shows the power of the test and the probability of type 2 errors for different effect sizes when

using a t-test at significance level 0.05 for sample sizes of 14 (the number of quarters likely to be available for

testing) and 20 (i.e. five complete years of test quarters) and 8. The sample size of 8 has been chosen because

it would be the degrees of freedom used in the modified t-test if alpha was 0.5 and the sample size was 14. If

alpha is close to 0, then the power will be close to that of a test with sample size 14. If alpha is between 0 and

0.5, then the power will be between the power of the tests carried out with sample sizes 8 and 14. If alpha is

greater than 0.5, then the power will be lower than the power of the test carried out using a sample size of 8.

To get an idea of the effect size in the current revisions hypothesis test, effect sizes based on the current

revisions analysis are:

Annual comparisons:

Preliminary GDP estimate (at t+25d) compared with the third GDP estimate (at t+89d): -0.7 (same as

0.7)

Second GDP estimate (t+58 d) compared with the third GDP estimate (t+89 d): -0.3 (same as 0.3)

Third GDP estimate (t+89 d) compared with the estimate after 3 years: 0.4

Quarterly comparisons:

Preliminary GDP estimate (at t+25d) compared with the third GDP estimate (at t+89d): 0.3

Second GDP estimate (t+58 d) compared with the third GDP estimate (t+89 d): 0.1

Third GDP estimate (t+89 d) compared with the estimate after 3 years: (same as 0.1)

To get an idea of alpha in the current revisions hypothesis test, alpha based on the current revisions analysis

are:

Annual comparisons:

Preliminary GDP estimate (at t+25d) compared with the third GDP estimate (at t+89d): -0.1 (same as

0.1)


Month 3 estimate (t+89 d) compared with the estimate after 3 years: 0.0

Quarterly comparisons:

Preliminary GDP estimate (at t+25d) compared with the third GDP estimate (at t+89d): 0.0


Third GDP estimate (t+89 d) compared with the estimate after 3 years: (same as 0.1) 0.4

Figure 1: Power of the t-test for given sample sizes and effect sizes and a significance level

of 0.05.

Source: UK Office for National Statistics

A common threshold for acceptable power is 80%. Figure 2 shows the sample size that would be required to

achieve a power of 80% for given effect sizes and a significance level of 0.05.

Figure 2: Sample size required to achieve 80% power for different effect sizes and a

significance level of 0.05.

Source: UK Office for National Statistics

Recommendation

The initial results suggest that the GDP t+30 flash estimate has a low effect size. The recommendation is

therefore that a student’s t-test would not be used as a quality acceptance criterion, due to the risk of a type II

error. Instead, it is recommended that appropriate boundaries for the size of the revision should be set.

Annex C: US t+30, t+60 and t+90 estimates of quarter-on-quarter GDP growth, and the associated revisions to the t+30 estimates

Table 9: GDP t+30 estimates and revisions for the US


NB: US publishes annualised quarter-on-quarter growth rates. For comparison here the annualised growth rates have been transformed back to plain quarter-on-quarter growth rates which are comparable with the ones given for the euro area and the EU.

Source: US Bureau of Economic Analysis

t+30 t+60 t+90 t+60 t+90

2012Q1 0.55 0.46 0.46 -0.08 -0.08

2012Q2 0.38 0.43 0.42 0.05 0.04

2012Q3 0.50 0.66 0.77 0.16 0.27

2012Q4 -0.04 0.03 0.09 0.07 0.13

2013Q1 0.62 0.59 0.44 -0.03 -0.18

2013Q2 0.71 0.92 0.91 0.21 0.20

2013Q3 0.71 0.89 1.02 0.18 0.31

2013Q4 0.80 0.59 0.65 -0.21 -0.15

2014Q1 0.03 -0.25 -0.74 -0.27 -0.77

2014Q2 0.97 1.03 1.13 0.05 0.16

2014Q3 0.88 0.96 1.22 0.08 0.34

2014Q4 0.65 0.54 0.55 -0.11 -0.10

2015Q1 0.06 -0.19 -0.04 -0.25 -0.10

2015Q2 0.58 0.91 0.97 0.33 0.39

0.01 0.03

0.15 0.23

0.18 0.29Root of the mean squared errors (RMSQE)


Average revision


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Annex D: The EU28 GDP growth and economic sentiment indicator

Figure 3: The year-on-year seasonally adjusted GDP growth rates (upper graph) and the

seasonally adjusted economic sentiment index (ESI, lower graph) for the EU, for the

endogenous group and the exogenous group

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Table 10: An ARIMAX model for estimating the 'residual' GDP for the EU28 in 2015Q4

Dependent Variable: EU28_ENDO Method: Least Squares Date: 01/28/16 Time: 18:21 Sample (adjusted): 2003Q2 2015Q3 Included observations: 50 after adjustments Convergence achieved after 10 iterations Variable Coefficient Std. Error t-Statistic Prob. ESI_ENDO_EU28_SA 0.292212 0.038018 7.686121 0.0000 C -28.00812 3.865700 -7.245292 0.0000 AR(1) 0.823405 0.077576 10.61418 0.0000 R-squared 0.925903 Mean dependent var 1.416924 Adjusted R-squared 0.922750 S.D. dependent var 2.867556 S.E. of regression 0.797004 Akaike info criterion 2.442210 Sum squared resid 29.85511 Schwarz criterion 2.556931 Log likelihood -58.05525 Hannan-Quinn criter. 2.485897 F-statistic 293.6533 Durbin-Watson stat 2.026317 Prob(F-statistic) 0.000000 Inverted AR Roots .82

Figure 4: The fit of the model against the original values and the model residuals

-3

-2

-1

0

1

2

-8

-4

0

4

8

03 04 05 06 07 08 09 10 11 12 13 14 15

Residual Actual Fitted

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